Question: In the right triangle shown, $AC = 4$ and $AB = 10$. What is $BC$ ? $A$ $C$ $B$ $4$ $?$ $10$
We know $a^2 + b^2 = c^2$ We want to find $a$ ; let $b = 4$ and $c = 10$ So $a^2 = c^2 - b^2 = 10^2 - 4^2 = 84$ Then, $a = \sqrt{84}$ Simplifying the radical gives $a = 2\sqrt{21}.$